Electromagnetic Interaction traced to Dirac Equation

An international group of physicists has traced the origin of an electromagnetic interaction to the Dirac equation, a fundamental equation of quantum physics.

The interaction couples the spin of the electron to the angular momentum of the electromagnetic field and it is responsible for a variety of phenomena in a large class of technologically important materials.

In addition to charge, electrons have spin. By understanding and using the different states achieved when an electron’s spin rotates, researchers could potentially increase information storage capacity in computers, for example.

Surendra Singh, professor of physics, and Bellaiche were part of the U of A team that proposed in 2013 that the angular momentum of an electromagnetic field can directly couple to the spin of an electron to produce a physical energy. This direct coupling explains known, subtle phenomena in magnetoelectric materials and predicts effects that have not yet been experimentally observed.

“For a long time, scientists explained these effects by using only the so-called spin-orbit coupling,” Singh said. “Our paper shows that the angular magnetoelectric interaction also contributes to these effects and that this term, along with spin-orbit coupling, follows naturally from a more exact theory of electron-light. It just had been ignored for so long.”

Physical Review B – Relativistic interaction Hamiltonian coupling the angular momentum of light and the electron spin


On the basis of the Dirac equation, a relativistic interaction Hamiltonian is derived which linearly couples the angular momentum density j of the electromagnetic (EM) field and the electron’s spin σ. The expectation value of this novel Hamiltonian is demonstrated to be precisely the recently proposed energy coupling the EM angular momentum density and magnetic moments [A. Raeliarijaona et al., Phys. Rev. Lett. 110, 137205 (2013)]. This previously overlooked Hamiltonian is also found to naturally result in the exact analytical form of the interaction energy inherent to the inverse Faraday effect, therefore demonstrating its relevance and easy use for the derivation of other complex magneto-optical and magnetoelectric effects originating from electron spin-light angular momentum couplings.